Tuesday 12 March 2013 20.39 EDT
First published on Tuesday 12 March 2013 20.39 EDT

Michael Gove challenged Theresa May to stop undermining David Cameron when he spoke out at a meeting on Tuesday of the Conservative political cabinet against prominent Tories who are promoting their leadership credentials.

In a sign of Downing Street's extreme irritation with the home secretary, who set out her political creed in a wide-ranging speech on Saturday, the education secretary made clear that such interventions played into the hands of opponents.

The move by Gove, which came as May and the education secretary achieved a significant victory in killing off No 10's plans for a minimum alcohol price of 45p a unit, shows that No 10 believes the growing party indiscipline has spread to the highest levels of the cabinet.

It is understood that Gove did not name May but left the political cabinet in no doubt that he had the home secretary in mind after her high-profile speech at the weekend in which she spoke way beyond her formal brief and set out her thoughts on what she called the three pillars of Conservatism.

The intervention by Gove was dismissed by allies of May who pointed out that the prime minister had approved her speech to a conference organised by the ConservativeHome website at 5pm on Friday. Cameron suggested some changes that were incorporated by the home secretary.

Sources close to May say it is wrong to link her speech to the recent speculation about the prime minister's future. The home secretary accepted the invitation to speak at the conference last November long before the claims by some Tory MPs that they are planning to trigger a no-confidence vote in the prime minister later this summer.

The rare personal blue-on-blue attack came hours before Tory MPs were given a stern warning by their Australian general election guru, Lynton Crosby, in front of Cameron, to decide whether they want to act as "commentators" on Twitter or "participants" in the runup to voting in 2015.

At a meeting of the Conservative parliamentary party, Crosby, who is a famed disciplinarian, said the general election was eminently winnable.

But he added that the constant sniping against Cameron on Twitter and the airwaves was unhelpful and playing into the hands of Labour.

The independent-minded MP Sarah Wollaston responded by complaining to Cameron that she learned about the warning from the Daily Mail's website hours earlier. Wollaston said on Twitter at the weekend that the prime minister should open up his inner circle, claiming it was too posh.

Kris Hopkins, the Tory MP for Keighley, was one of the MPs in marginal seats who hit out at the critics.

James Forsyth, the political editor of the Spectator, said Hopkins criticised MPs who have been highlighting their leadership credentials as "self indulgent buffoons".

MPs were given a taste of Crosby's tactics when Cameron said he would outline a 10-point checklist of Tory achievements that will form the bedrock of the party's campaigning over the next two years.

The achievements include cutting the fiscal deficit by a quarter; reducing immigration by a third; 1m new jobs in the private sector; cutting the EU budget for the first time; vetoing an EU treaty for the first time; promising an in/out referendum on Britain's EU membership; new laws to place householders on the lowest energy tariff; creating a single tier pension; introducing a £75,000 cap on the costs of longterm care; and taking 2 million people out of tax with an average £600 cut in tax bills for 24m people.

One Tory source said: "These are difficult times but we can be proud that we have achieved a great deal."

The decision of Gove – who is one of the prime minister's closest cabinet allies – to confront May shows that the leadership believes the home secretary is fuelling backbench disloyalty by staking out territory for a leadership contest.

May insists she is loyal but is being a "realist" in the highly unlikely event of a contest.